Why Quasicategories?

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Homotopy Coherent Groups and Quasi-Categories

Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.

Sets of Left Homotopy Classes: The Homotopy Relation in a Model Category

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Homotopical Algebra: Introduction

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Adjunction between Simplicial Sets and Enriched Categories

Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.

Homotopical Algebra: The Homotopy Category of a Model Category

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Left Homotopy as an Equivalence Relation: The Homotopy Relation in a Model Category

Explores the left homotopy relation as an equivalence relation in model categories.